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 A bit about Elo ratings.en.wikipedia.org I think it would be useful for every gameknot team captain who uses Elo ratings in setting up pairings to read that Wiki entry and to know the formula to calculate the probable outcome of a pairing based on Elo rating. This system considers only the difference in Elo ratings, not their absolute value. In the Elo system, a player with a 1000 Elo rating has the same chance to win against a player with a 1100 Elo rating as a player with 2000 Elo rating has to win against a player with a 2100 Elo rating. The formula gives the probability that the player with the lower rating will win. The probability for the stronger player winning is 1 minus the probability of the lower-rated player winning. Draws are not considered. I do not know how not considering draws affects the calculation, but my guess would be that it means that differences in Elo rating are more accurately predictive of outcomes for higher-rated players than for lower-rated players. The curve shown in that Wiki article on the winning probability for the weaker and stronger player based on difference in Elo rating is caculated by the formula given below. Formula: Divide the difference in Elo ratings by 400. Take 10 to that power and add 1. Divide 1 by that result. For those who remember high school math: y = 1/{[1/(10^x/400)] +1}; where y is the probability of the lower-rated player winning, x is the absolute value of the difference in Elo ratings, and the ^ symbol means the exponent, or to the power of. This messaging system is not well set up for showing mathematical formulas. Examples: 0 difference in Elo rating. 10^0/400 = 10^0 = 1; 1 + 1 = 2; 1/2 = .5, or 50 percent. 50 difference in Elo rating. 10^50/400 = 10^.125 = 1.33; 1.33 + 1 = 2.33; 1/2.33 = .43, or 43% 100 difference in Elo rating. 10^100/400 = 10^.25 = 1.78; 1.78 + 1 = 2.78; 1/2.78 = .36, or 36% 150 difference in Elo rating. 10^150/400 = 10^.375 = 2.37; 2.37 + 1 = 3.37; 1/3.37 = .30, or 30% 200 difference in Elo rating. 10^200/400 = 10^.5 = 3.16; 3.16 + 1 = 4.16; 1/4.16 = .24, or 24% 300 difference in Elo rating. 10^300/400 = 10^.75 = 5.62; 5.62 + 1 = 6.62; 1/6.62 = .15, or 15% 400 difference in Elo rating. 10^400/400 = 10^1 = 10 + 1 = 11; 1/11= .09, or 9% I was surprised that the winning probability did into decrease more quickly for the lower-rated player. A 1500-rated player should win around 10% of the games with a 1900-rated player according to this calculation. I also point out that losses in the last two games between two players who have played 20 games are not accurately predictive of the outcome of the next match between those two players if the overall record over those 20 games is an equal number of wins and losses for both players. However, a stong trend of an increased percentage of wins for one player over 20 games might well be predictive. |
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Correction |
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orkneylad The version i got also told me how you were a retired professor of biology for well over 30 years from Texas and how you like to teach. And you ended it by writing after this lesson. which i found insulting i felt like i had been dragged into the principles office for a dressing down. This is because i sent a decline for a match. Let me tell you professor i am not one of your students in Texas and do not send me anymore pm. |
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Perhaps an apology is in order. When I mention being a retired professor, it is as an apology and excuse, not a boast. I have lived a life in which professors are a dime a dozen. I mention that I am a professor only to explain my perhaps otherwise inexplicable urge to explain things to people who may not even want to know. I spent my entire career doing that. |
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surprising that the percentage drop quickly with each 50 point difference. Thanks for posting this, Mike. |
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Russian Putin will never apologize. The king was happy because his kingdom was much more peaceful when the warlords play chess without fighting. As a matter of fact, chess is a warlike game but without death and destruction. Since there is no death and destruction unlike the war in Ukraine, nobody needs to apologize each other. We all should maintain this peaceful tradition of playing chess, IMHO. |
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mikemate The post is fine and very informative but i did not like my version as i have pointed out in my last post. I was sent a match from orkneylad using the above Elo rating and as i do not use this system and he got a decline and i do not think it went down well so he got in touch with my captain. I do not think many of us will go to all this trouble to make a match we do not all have the time. Geoff |
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A clarification It is not true that the decline did not go down well with me. Challenges get declined all the time. I was just enthusiastic about having discovered what Elo ratings predict, which I had just learned. I used this one example to show that Elo ratings predict something different than the reason Geoff used to decline my challenge. I do not suggest that people use the Elo rating formula in making matches, although they are welcome to do so. I posted it because I found it interesting and thought others might as well. It is little work to calculate expected outcomes if you know the formula and have a calculator, whether one wants to go to the trouble or not. I hope I have not poisoned relations between our team and THE ROYAL KNIGHTS. I am sorry that this difference in opinion went public. In my original posting I purposely avoided mentioning names or events. |
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Michael I've never understood the need to go public over "perceived slights" which are usually a misunderstanding but it happens, you've never had problems with my declines and I don't do many , I happen to like your challenges they wake me up ! Make me think lol The stories are true I once had a job at the orange juice factory... but I got canned because I couldn't "concentrate" |
